Basics of Kolmogorov-Arnold Networks (KAN)

This repo contains notebooks with toy examples to build intuitive understanding of Kolmogorov-Arnold Networks (KAN). The repo contains a series of Jupyter notebooks to explore concepts and code to build KANs, designed to build your understanding of KANs gradually, starting from the basics of B-splines used as activation functions and progressing through more complex scenarios including symbolic regression.

Original paper: Liu et al. 2024, KAN: Kolmogorov-Arnold Networks

Original repository: Prateek Gupta

About the Tutorials

With the help of toy examples, notebooks are structured to help in understanding both the theoretical underpinnings and practical applications of KANs.

1. B-Splines for KAN:

   • Understanding the mathematical construction of B-splines.
   • Exploring how B-splines are used for functional approximation.

2. Deeper KANs

   • Constructing and understanding [1, 1, 1, ..., 1] KAN configurations.
   • Implementing and exploring backpropagation through stacked splines.

3. Grid Manipulation in KANs

   • How to expand model's capacity through grid manipulation.
   • How KANs prevent catastrophic forgetting in continual learning?

4. Symbolic Regression using KANs

   • Training KANs with fixed symbolic activation functions.
   • Understanding the implications of symbolic regression within neural networks.

Prerequisites

To follow these tutorials, you should have a basic understanding of machine learning concepts and be familiar with Python programming. Experience with PyTorch and Jupyter Notebooks is also recommended.

Setup (Windows, macOS, Linux)

Follow these steps to run the notebooks:

Option A: Using conda (recommended)

1. Install Miniconda or Anaconda
2. From the project root, create the environment:

conda env create -f environment.yml

3. Activate the environment:

conda activate kan-tutorial

4. (Optional) Create a .env from the example and adjust as desired:

copy example.env .env   # on Windows
# cp example.env .env   # on macOS/Linux

5. Launch JupyterLab:

jupyter lab

Option B: Using pip + venv

1. Create and activate a virtual environment:

python -m venv .venv
# Windows
.\.venv\Scripts\activate
# macOS/Linux
# source .venv/bin/activate

2. Install requirements:

pip install -r requirements.txt

3. (Optional) Copy environment example:

copy example.env .env   # on Windows
# cp example.env .env   # on macOS/Linux

4. Start JupyterLab:

jupyter lab

Notes

• The notebooks and utils.py use torch, numpy, and matplotlib.
• The provided environment.yml pins Python 3.10 and CPU-only PyTorch by default. If you have a CUDA-capable GPU, replace cpuonly with an appropriate CUDA package per PyTorch installation instructions.

Repositories of Interest

Original repository by Prateek Gupta. https://github.com/pg2455/KAN-Tutorial

FastKAN: Very Fast Kolmogorov-Arnold Network via Radial Basis Functions. https://github.com/ZiyaoLi/fast-kan

Efficient KAN: An Efficient Implementation of Kolmogorov-Arnold Network. https://github.com/Blealtan/efficient-kan